Methods for Discrete Design Optimization

2005 ◽  
Author(s):  
Marcus Pettersson ◽  
Johan Andersson ◽  
Petter Krus
Keyword(s):  
Design Optimization ◽  
Industrial Robot ◽  
Gradient Methods ◽  
Simulation Models ◽  
Gradient Algorithm ◽  
Complex Method ◽  
Performance Metric ◽  
Design Variables ◽  
Natural Choice ◽  
Discrete Complex

One area in design optimization is component based design where the designer has to choose between many different discrete alternatives. These types of problems have discrete character and in order to admit optimization an interpolation between the alternatives is often performed. However, in this paper a modified version of the non-gradient algorithm the Complex method is developed where no interpolation between alternatives is needed. Furthermore, the optimization algorithm itself is optimized using a performance metric that measures the effectiveness of the algorithm. In this way the optimal performance of the proposed discrete Complex method has been identified. Another important area in design optimization is the case of optimization based on simulations. For such problems no gradient information is available, hence non-gradient methods are therefore a natural choice. The application for this paper is the design of an industrial robot where the system performance is evaluated using comprehensive simulation models. The objective is to maximize performance with constraints on lifetime and cost, and the design variables are discrete choices of gear boxes for the different axes.

Optimizing Optimization for Design Optimization

2003 ◽  
Author(s):  
Petter Krus ◽  
Johan Andersson
Keyword(s):  
Product Development ◽  
Design Optimization ◽  
Optimization Algorithm ◽  
Development Process ◽  
Gradient Methods ◽  
Product Development Process ◽  
Optimization Approach ◽  
Holistic View ◽  
Direct Search Methods ◽  
Natural Choice

Design optimization is becoming and increasingly important tool for design. In order to have an impact on the product development process it must permeate all levels of the design in such a way that a holistic view is maintained through all stages of the design. One important area is in the case of optimization based on simulation, which generally requires non-gradient methods and as a consequence direct-search methods is a natural choice. The idea in this paper is to use the design optimization approach in the optimization algorithm itself in order to produce an efficient and robust optimization algorithm. The result is a single performance index to measure the effectiveness of an optimization algorithm, and the COMPLEX-RF optimization algorithm, with optimized parameters.

scholarly journals Brass Instruments Design Using Physics-Based Sound Simulation Models and Surrogate-Assisted Derivative-Free Optimization

2016 ◽  
Author(s):  
Robin Tournemenne ◽  
Jean-François Petiot ◽  
Bastien Talgorn ◽  
Michael Kokkolaras
Keyword(s):  
Design Optimization ◽  
Search Algorithm ◽  
Rank Order ◽  
Computational Cost ◽  
Simulation Models ◽  
Function Evaluation ◽  
Brass Instruments ◽  
Design Variables ◽  
Direct Search Algorithm ◽  
Sound Simulation

This paper presents a method for design optimization of brass wind instruments. The shape of a trumpet’s bore is optimized to improve intonation using a physics-based sound simulation model. This physics-based model consists of an acoustic model of the resonator (input impedance), a mechanical model of the excitator (the lips of a virtual musician) and a model of the coupling between the excitator and the resonator. The harmonic balance technique allows the computation of sounds in a permanent regime, representative of the shape of the resonator according to control parameters of the virtual musician. An optimization problem is formulated, in which the objective function to be minimized is the overall quality of the intonation of the different notes played by the instrument (deviation from the equal-tempered scale). The design variables are the physical dimensions of the resonator. Given the computationally expensive function evaluation and the unavailability of gradients, a surrogate-assisted optimization framework is implemented using the mesh adaptive direct search algorithm (MADS). Surrogate models are used both to obtain promising candidates in the search step of MADS and to rank-order additional candidates generated by the poll step of MADS. The physics-based model is then used to determine the next design iterate. Two examples (with two and five design optimization variables, respectively) are presented to demonstrate the approach. Results show that significant improvement of intonation can be achieved at reasonable computational cost. The implementation of this method for computer-aided instrument design is discussed, considering different objective functions or constraints based on intonation but also on the timbre of the instrument.

scholarly journals Brass Instruments Design Using Physics-Based Sound Simulation Models and Surrogate-Assisted Derivative-Free Optimization

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Robin Tournemenne ◽  
Jean-François Petiot ◽  
Bastien Talgorn ◽  
Michael Kokkolaras ◽  
Joël Gilbert
Keyword(s):  
Design Optimization ◽  
Search Algorithm ◽  
Rank Order ◽  
Computational Cost ◽  
Simulation Models ◽  
Problem Formulation ◽  
Function Evaluation ◽  
Design Variables ◽  
Direct Search Algorithm ◽  
Sound Simulation

This paper presents a method for design optimization of brass wind instruments. The shape of a trumpet's bore is optimized to improve intonation using a physics-based sound simulation model. This physics-based model consists of an acoustic model of the resonator, a mechanical model of the excitator, and a model of the coupling between the excitator and the resonator. The harmonic balance technique allows the computation of sounds in a permanent regime, representative of the shape of the resonator according to control parameters of the virtual musician. An optimization problem is formulated in which the objective function to be minimized is the overall quality of the intonation of the different notes played by the instrument. The design variables are the physical dimensions of the resonator. Given the computationally expensive function evaluation and the unavailability of gradients, a surrogate-assisted optimization framework is implemented using the mesh adaptive direct search algorithm (MADS). Surrogate models are used both to obtain promising candidates in the search step of MADS and to rank-order additional candidates generated by the poll step of MADS. The physics-based model is then used to determine the next design iterate. Two examples (with two and five design optimization variables) demonstrate the approach. Results show that significant improvement of intonation can be achieved at reasonable computational cost. Finally, the perspectives of this approach for computer-aided instrument design are evoked, considering optimization algorithm improvements and problem formulation modifications using for instance different design variables, multiple objectives and constraints or objective functions based on the instrument's timbre.

scholarly journals Hybrid Seven-bar Press Mechanism

2018 ◽  
Vol 12 (3) ◽  
pp. 181-187
Author(s):  
M. Erkan Kütük ◽  
L. Canan Dülger
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Design Optimization ◽  
Hybrid System ◽  
Degrees Of Freedom ◽  
Dimensional Synthesis ◽  
Design Variables ◽  
Optimization Study ◽  
Metal Stamping

An optimization study with kinetostatic analysis is performed on hybrid seven-bar press mechanism. This study is based on previous studies performed on planar hybrid seven-bar linkage. Dimensional synthesis is performed, and optimum link lengths for the mechanism are found. Optimization study is performed by using genetic algorithm (GA). Genetic Algorithm Toolbox is used with Optimization Toolbox in MATLAB®. The design variables and the constraints are used during design optimization. The objective function is determined and eight precision points are used. A seven-bar linkage system with two degrees of freedom is chosen as an example. Metal stamping operation with a dwell is taken as the case study. Having completed optimization, the kinetostatic analysis is performed. All forces on the links and the crank torques are calculated on the hybrid system with the optimized link lengths

THE DETERMINATION OF DIGITAL WIENER FILTERS BY MEANS OF GRADIENT METHODS

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 310-326 ◽  
Author(s):  
R. J. Wang ◽  
S. Treitel
Keyword(s):  
Seismic Data ◽  
High Speed ◽  
Gradient Methods ◽  
Wiener Filter ◽  
Gradient Algorithm ◽  
Rapid Convergence ◽  
True Solution ◽  
Peripheral Device ◽  
Wiener Filters

The normal equations for the discrete Wiener filter are conventionally solved with Levinson’s algorithm. The resultant solutions are exact except for numerical roundoff. In many instances, approximate rather than exact solutions satisfy seismologists’ requirements. The so‐called “gradient” or “steepest descent” iteration techniques can be used to produce approximate filters at computing speeds significantly higher than those achievable with Levinson’s method. Moreover, gradient schemes are well suited for implementation on a digital computer provided with a floating‐point array processor (i.e., a high‐speed peripheral device designed to carry out a specific set of multiply‐and‐add operations). Levinson’s method (1947) cannot be programmed efficiently for such special‐purpose hardware, and this consideration renders the use of gradient schemes even more attractive. It is, of course, advisable to utilize a gradient algorithm which generally provides rapid convergence to the true solution. The “conjugate‐gradient” method of Hestenes (1956) is one of a family of algorithms having this property. Experimental calculations performed with real seismic data indicate that adequate filter approximations are obtainable at a fraction of the computer cost required for use of Levinson’s algorithm.

Barrier Function Method in Reliability Based Design Optimization

2005 ◽  
Vol 297-300 ◽  
pp. 1882-1887
Author(s):  
Tae Hee Lee ◽  
Jung Hun Yoo
Keyword(s):  
Design Optimization ◽  
Barrier Function ◽  
Reliability Index ◽  
Feasible Solution ◽  
Reliability Based Design Optimization ◽  
User Requirement ◽  
Mean Values ◽  
Reliability Based Design ◽  
Design Variables ◽  
Reliability Method

In practical design applications, most design variables such as thickness, diameter and material properties are not deterministic but stochastic numbers that can be represented by their mean values with variances because of various uncertainties. When the uncertainties related with design variables and manufacturing process are considered in engineering design, the specified reliability of the design can be achieved by using the so-called reliability based design optimization. Reliability based design optimization takes into account the uncertainties in the design in order to meet the user requirement of the specified reliability while seeking optimal solution. Reliability based design optimization of a real system becomes now an emerging technique to achieve reliability, robustness and safety of the design. It is, however, well known that reliability based design optimization can often have so multiple local optima that it cannot converge into the specified reliability. To overcome this difficulty, barrier function approach in reliability based design optimization is proposed in this research and feasible solution with specified reliability index is always provided if a feasible solution is available. To illustrate the proposed formulation, reliability based design optimization of a bracket design is performed. Advanced mean value method and first order reliability method are employed for reliability analysis and their optimization results are compared with reliability index approach based on the accuracy and efficiency.

Adaptive Complex Method for Efficient Design Optimization

2007 ◽  
Author(s):  
Marcus Pettersson ◽  
Johan O¨lvander
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Global Optimum ◽  
Direct Search ◽  
Complex Method ◽  
Efficient Design ◽  
Direct Search Methods ◽  
Simulation Based ◽  
Set Of Points ◽  
Quasi Newton

Box’s Complex method for direct search has shown promise when applied to simulation based optimization. In direct search methods, like Box’s Complex method, the search starts with a set of points, where each point is a solution to the optimization problem. In the Complex method the number of points must be at least one plus the number of variables. However, in order to avoid premature termination and increase the likelihood of finding the global optimum more points are often used at the expense of the required number of evaluations. The idea in this paper is to gradually remove points during the optimization in order to achieve an adaptive Complex method for more efficient design optimization. The proposed method shows encouraging results when compared to the Complex method with fix number of points and a quasi-Newton method.

Aerodynamic Automobile Shape Optimization by Incorporating Reverse Shape Design Method With CFD Analysis

2017 ◽  
Author(s):  
Kisun Song ◽  
Kyung Hak Choo ◽  
Jung-Hyun Kim ◽  
Dimitri N. Mavris
Keyword(s):  
Design Optimization ◽  
Aerodynamic Drag ◽  
Design Method ◽  
Shape Design ◽  
Cfd Analysis ◽  
Simple Arithmetic ◽  
Design Variables ◽  
3D Geometry ◽  
Geometric Entity ◽  
Aerodynamic Drag Reduction

In modern automotive industry market, there have been a lot of state-of-art methodologies to perform a conceptual design of a car; functional methods and 3D scanning technology are widely used. Naturally, the issues frequently boiled down to a trade-off decision making problem between quality and cost. Besides, to incorporate the design method with advanced optimization methodologies such as design-of-experiments (DOE), surrogate modeling, how efficiently a method can morph or recreate a vehicle’s shape is crucial. This paper accomplishes an aerodynamic design optimization of rear shape of a sedan by incorporating a reverse shape design method (RSDM) with the aforementioned methodologies based on CFD analysis for aerodynamic drag reduction. RSDM reversely recovers a 3D geometry of a car from several 2D schematics. The backbone boundary lines of 2D schematic are identified and regressed by appropriate interpolation function and a 3D shape is yielded by a series of simple arithmetic calculations without losing the detail geometric features. Besides, RSDM can parametrize every geometric entity to efficiently manipulate the shape for application to design optimization studies. As the baseline, an Audi A6 is modeled by RSDM and explored through CFD analysis for model validation. Choosing six design variables around the rear shape, 77 design points are created to build neural networks. Finally, a significant amount of CD reduction is obtained and corresponding configuration is validated via CFD.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

Design Optimization of RML Glove for Improved Grasp Performance

2018 ◽  
Author(s):  
Teja Vanteddu ◽  
Bijo Sebastian ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Design Optimization ◽  
Daily Living ◽  
Experimental Validation ◽  
Large Diameter ◽  
Future Research ◽  
Linkage Mechanism ◽  
Design Variables ◽  
Wide Range ◽  
Optimal Values ◽  
Optimal Set

This paper describes the design optimization of the RML Glove in order to improve its grasp performance. The existing design is limited to grasping objects of large diameter (> 110mm) due to its inability in attaining high bending angles. For an exoskeleton glove to be effective in its use as an assistive and rehabilitation device for Activities of Daily Living (ADL), it should be able to interact with objects over a wide range of sizes. Motivated by these limitations, the kinematics of the existing linkage mechanism was analyzed in detail and the design variables were identified. Two different cost functions were formulated and compared in their ability to yield optimal values for the design variables. The optimal set of design variables was chosen based on the grasp angles achieved and the resulting mechanism was simulated in CAD for feasibility testing. An exoskeleton mechanism corresponding to the index finger was manufactured with the chosen design variables and detailed experimental validation was performed to illustrate the improvement in grasp performance over the existing design. The paper ends with a summary of the experimental results and directions for future research.

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